Stellarator symmetry - Revision history

Admin at 09:45, 30 October 2015

2015-10-30T09:45:39Z

← Older revision		Revision as of 11:45, 30 October 2015
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	reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and		reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and
	not an ''inherent'' (natural) symmetry of stellarator plasmas.		not an ''inherent'' (natural) symmetry of stellarator plasmas.
	<ref>~~[http://dx.doi.org/10.1016/S0167-2789(97)00216-9~~ R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>		<ref>R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', [[doi:10.1016/S0167-2789(97)00216-9\|Physica D, '''112''' (1998) 275]]</ref>
	Therefore, it has the same status as [[axisymmetry]] in [[tokamak]]s.		Therefore, it has the same status as [[axisymmetry]] in [[tokamak]]s.

Admin at 08:00, 5 September 2013

2013-09-05T08:00:30Z

← Older revision		Revision as of 10:00, 5 September 2013
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	Stellarator symmetry is a property of typical [[~~Stellarator\|~~stellarator]] magnetic configurations.		Stellarator symmetry is a property of typical [[stellarator]] magnetic configurations.
	It is important to be aware that it is an ''imposed'' (artificial) symmetry,		It is important to be aware that it is an ''imposed'' (artificial) symmetry,
	reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and		reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and
	not an ''inherent'' (natural) symmetry of stellarator plasmas.		not an ''inherent'' (natural) symmetry of stellarator plasmas.
	<ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>		<ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>
	Therefore, it has the same status as [[~~Toroidal coordinates\|~~axisymmetry]] in [[~~Tokamak\|tokamaks~~]].		Therefore, it has the same status as [[axisymmetry]] in [[tokamak]]s.

	In a [[Toroidal coordinates\|cylindrical coordinate system]], it is expressed as follows for a scalar field:		In a [[Toroidal coordinates\|cylindrical coordinate system]], it is expressed as follows for a scalar field:

Admin at 18:49, 11 February 2013

2013-02-11T18:49:01Z

← Older revision		Revision as of 20:49, 11 February 2013
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	Stellarator symmetry is a property of typical [[Stellarator\|stellarator]] magnetic configurations.		Stellarator symmetry is a property of typical [[Stellarator\|stellarator]] magnetic configurations.
	It is important be aware that it is an ''imposed'' (artificial) symmetry,		It is important to be aware that it is an ''imposed'' (artificial) symmetry,
	reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and		reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and
	not an ''inherent'' (natural) symmetry of stellarator plasmas.		not an ''inherent'' (natural) symmetry of stellarator plasmas.

Admin at 11:48, 5 February 2011

2011-02-05T11:48:35Z

← Older revision		Revision as of 13:48, 5 February 2011
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	not an ''inherent'' (natural) symmetry of stellarator plasmas.		not an ''inherent'' (natural) symmetry of stellarator plasmas.
	<ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>		<ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>
			Therefore, it has the same status as [[Toroidal coordinates\|axisymmetry]] in [[Tokamak\|tokamaks]].

	In a [[Toroidal coordinates\|cylindrical coordinate system]], it is expressed as follows for a scalar field:		In a [[Toroidal coordinates\|cylindrical coordinate system]], it is expressed as follows for a scalar field:

Admin at 14:47, 2 February 2011

2011-02-02T14:47:30Z

← Older revision		Revision as of 16:47, 2 February 2011
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	Stellarator symmetry is a property of typical [[Stellarator\|stellarator]] magnetic configurations.		Stellarator symmetry is a property of typical [[Stellarator\|stellarator]] magnetic configurations.
			It is important be aware that it is an ''imposed'' (artificial) symmetry,
			reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and
			not an ''inherent'' (natural) symmetry of stellarator plasmas.
			<ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>

	In a [[Toroidal coordinates\|cylindrical coordinate system]], it is expressed as follows for a scalar field:		In a [[Toroidal coordinates\|cylindrical coordinate system]], it is expressed as follows for a scalar field:

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	:<math>\left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)}</math>		:<math>\left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)}</math>

	With ''N''-fold rotation symmetry around the ''Z'' axis, there are ''2N'' such planes. ~~<ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>~~		With ''N''-fold rotation symmetry around the ''Z'' axis, there are ''2N'' such planes.

	== References ==		== References ==
	<references/>		<references/>

Admin at 10:57, 12 June 2010

2010-06-12T10:57:06Z

← Older revision		Revision as of 12:57, 12 June 2010
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	:<math>\left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)}</math>		:<math>\left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)}</math>

	With ''N''-fold rotation symmetry around the ''Z'' axis, there are ''2N'' such planes. <ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', ~~Phys.~~ D, '''112''' (1998) 275]</ref>		With ''N''-fold rotation symmetry around the ''Z'' axis, there are ''2N'' such planes. <ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref>

	== References ==		== References ==
	<references/>		<references/>

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Stellarator symmetry is a property of typical [[Stellarator|stellarator]] magnetic configurations.
In a [[Toroidal coordinates|cylindrical coordinate system]], it is expressed as follows for a scalar field:

:<math>\psi(R,\phi,Z) = \psi(R,-\phi,-Z)\,</math>

with respect to the symmetry plane ''φ = 0''. Likewise, for a vector field:

:<math>\left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)}</math>

With ''N''-fold rotation symmetry around the ''Z'' axis, there are ''2N'' such planes. <ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Phys. D, '''112''' (1998) 275]</ref>

== References ==
<references/>